Accurate and continuous estimation of cognitive workload is fundamental to creating adaptive human-machine systems. However, designing architectures that balance representational capacity with computational efficiency has been challenging for practical deployment. This paper introduces 1BT, a One-Block Transformer for compact and efficient EEG-based cognitive workload assessment. The model aggregates multi-channel temporal sequences via a minimal latent bottleneck, using a single cross-attention module followed by lightweight self-attention. A controlled study involving 11 participants performing three cognitively diverse tasks (abstract reasoning, numerical problem-solving, and an interactive video game) was conducted with continuous EEG recordings across two workload levels. Systematic architectural analysis identifies the most compact configuration that preserves high performance, while substantially lowering computational cost. The final model achieves high workload classification performance with under 0.5 million parameters and 0.02 GFLOPs, paving the way for a design direction for real-time cognitive workload monitoring in resource-constrained settings.